Showing papers on "Constant (mathematics) published in 2001"

Direct and Indirect Effects

Abstract: The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and practical difficulties (in nonlinear models), because they cannot be isolated by holding certain variables constant. This paper presents a new way of defining the effect transmitted through a restricted set of paths, without controlling variables on the remaining paths. This permits the assessment of a more natural type of direct and indirect effects, one that is applicable in both linear and nonlinear models and that has broader policy-related interpretations. The paper establishes conditions under which such assessments can be estimated consistently from experimental and nonexperimental data, and thus extends path-analytic techniques to nonlinear and nonparametric models.

On the Existence of Globally Defined Weak Solutions to the Navier—Stokes Equations

Abstract: We prove the existence of globally defined weak solutions to the Navier—Stokes equations of compressible isentropic flows in three space dimensions on condition that the adiabatic constant satisfies $ \gamma > 3/2 $ .

Interacting Quintessence

Abstract: We demonstrate that a suitable coupling between a quintessence scalar field and a pressureless cold dark matter (CDM) fluid leads to a constant ratio of the energy densities of both components which is compatible with an accelerated expansion of the Universe.

Use of constant comparative analysis in qualitative research.

Abstract: This article describes the application of constant comparative analysis, which is one method that can be used to analyse qualitative data. The need for data analysis to be congruent with the overall research design is highlighted.

Evaluation and generalization of temperature‐based methods for calculating evaporation

Abstract: Seven temperature-based equations, each representing a typical form, were evaluated and compared for determining evaporation at two climatological stations (Rawson Lake and Atikokan) in north-western Ontario, Canada The comparison was first made using the original constant values involved in each equation, and then using the recalibrated constant values The results show that when the original constant values were used, larger biases existed for most of the equations for both stations When recalibrated constant values were substituted for the original constant values, six of the seven equations improved for both stations Using locally calibrated parameter values, all seven equations worked well for determining mean seasonal evaporation values For monthly evaporation values, the modified Blaney–Criddle method produced least error for all months for both stations, followed by the Hargreaves and Thornthwaite methods The Linacre, Kharrufa and Hamon methods showed a significant bias in September for both stations With properly determined constant values, the modified Blaney–Criddle, the Hargreaves and Thornthwaite methods can be recommended for estimating evaporation in the study region, as far as temperature-based methods are concerned Copyright © 2001 John Wiley & Sons, Ltd

The Octagon Abstract Domain

Abstract: This article presents a new numerical abstract domain for static analysis by abstract interpretation. It extends a former numerical abstract domain based on Difference-Bound Matrices and allows us to represent in- variants of the form (fafy < c), where a and y are program variables and c is a real constant.

ASCE's standardized reference evapotranspiration equation.

Abstract: The ASCE Evapotranspiration in Irrigation and Hydrology Committee (ASCE-ET) is recommending, for the intended purpose of establishing uniform evapotranspiration (ET) estimates and transferable crop coefficients, two Standardized Reference Evapotranspiration Surfaces : (1) a short crop (similar to grass) and (2) a tall crop (similar to alfalfa), and one Standardized Reference Evapotranspiration Equation . The standardized equation is derived from the ASCE-Penman Monteith equation, by simplifying several terms within that equation. The standardized equation, with appropriate constants provided in an accompanying table, is used to calculate evapotranspiration for the standardized short reference (ET os ) and/or evapotranspiration for the standardized tall reference (ET rs ). One constant is in the numerator and one is in the denominator. The constant in the right-hand side of the numerator (C n ) is a function of the time step and aerodynamic resistance (i.e., reference type). The constant in the denominator (C d ) is a function of the time step, bulk surface resistance, and aerodynamic resistance (the latter two terms vary with reference to type, time step, and daytime/nighttime).

Local theory in critical spaces for compressible viscous and heat-conductive gases

Abstract: We are concerned with local existence and uniqueness of solutions for a general model of viscous and heat-conductive gases with low regularity assumptions on the initial data (the velocity and the temperature may be discontinuous). Local well-posedness is showed to hold in spaces which are critical with respect to the scaling of the equations, provided that the initial density is close enough to a positive constant. When initial data are a trifle more regular, local well-posedness holds for any initial density bounded away from zero. This former result lies on new estimates for linear heat equations with a non constant diffusion coefficient.

Dc-to-dc converter

Abstract: A transformer has a primary winding connected between a pair of dc input terminals via an on-off switch, and a secondary winding connected between a pair of dc output terminals via a rectifying and smoothing circuit The output voltage applied from the rectifying and smoothing circuit to the load is held constant by switching the input voltage through feedback control The switch is driven in either of two different prescribed modes depending upon whether the converter is under normal or light load In order to ascertain the load magnitude a flyback period determination circuit is connected to a tertiary winding of the transformer for providing a signal indicative of a flyback period during which a flyback voltage exists across the transformer tertiary after the switch is turned off each time Each flyback period is compared with two different reference periods of time for hysteretic determination of whether the converter is under normal or light load Several other embodiments are disclosed

Ab initio simulation of charged slabs at constant chemical potential

Abstract: We present a practical scheme for performing ab initio supercell calculations of charged slabs at constant electron chemical potential μ, rather than at constant number of electrons Ne To this end, we define the chemical potential relative to a plane (or “reference electrode”) at a finite distance from the slab (the distance should reflect the particular geometry of the situation being modeled) To avoid a net charge in the supercell, and thus make possible a standard supercell calculation, we restore the electroneutrality of the periodically repeated unit by means of a compensating charge, whose contribution to the total energy and potential is subtracted afterwards The “constant μ” mode enables one to perform supercell calculation on slabs, where the slab is kept at a fixed potential relative to the reference electrode We expect this to be useful in modeling many experimental situations, especially in electro-chemistry

Consequences on variable Λ-models from distant type Ia supernovae and compact radio sources

Abstract: We study the magnitude-redshift relation for the type?Ia supernovae data and the angular size-redshift relation for the updated compact radio sources data (from Gurvits et?al) by considering four variable ?-models: ?~S-2, ?~H2, ?~? and ?~t-2. It is found that all the variable ?-models, as well as the constant ?-Friedmann model, fit the supernovae data equally well with ?2/dof?1 and require non-zero, positive values of ? and an accelerating expansion of the universe. The estimates of the density parameter for the variable ?-models are found to be higher than those for the constant ?-Friedmann model. From the compact radio sources data, it is found, by assuming the no-evolution hypothesis, that the Gurvits et al model (Friedmann model with ? = 0) is not the best-fitting model for the constant ? case. The best-fitting Friedmann model (with constant ?) is found to be a low-density, vacuum-dominated accelerating universe. The fits of this data set to the (variable, as well as, constant ?-) models are found to be very good with ?2/dof?0.5 and require non-zero, positive values of ? with either sign of the deceleration parameter. However, for realistic values of the matter density parameter, the only interesting solutions are (a) estimated from the supernovae data: the best-fitting solutions for the flat models (including the constant ? case); (b) estimated from the radio sources data: the global best-fitting solutions for the models ?~H2 and ?~?, the best-fitting solution for the flat model with ? = {}constant and the Gurvits et al model. It is noted that, as in the case of recent cosmic microwave background analyses, the data sets seem to favour a spherical universe (k>0).

Diameters of finite simple groups: sharp bounds and applications

Abstract: Let G be a finite simple group and let S be a normal subset of G. We determine the diameter of the Cayley graph r(G, S) associated with G and S, up to a multiplicative constant. Many applications follow. For example, we deduce that there is a constant c such that every element of G is a product of c involutions (and we generalize this to elements of arbitrary order). We also show that for any word w = w(xl,..., xd), there is a constant c = c(w) such that for any simple group G on which w does not vanish, every element of G is a product of c values of w. From this we deduce that every verbal subgroup of a semisimple profinite group is closed. Other applications concern covering numbers, expanders, and random walks on finite simple groups.

Size-dependent Rigidities of Nanosized Torsional Elements

Abstract: A theory for the prediction of the size dependence of torsional rigidities of nanosized structural elements is developed. It is shown that, to a very good approximation, the torsional rigidity (D) of a nanosized bar differs from the prediction of standard continuum mechanics $(D_c)$ as $(D-D_c)/D_c = A h_0/a$ where A is a non-dimensional constant, a is the size scale of the cross-section of the bar and $h_0$ is a material length equal to the ratio of the surface elastic constant to the bulk elastic constant. The theory developed is compared with direct atomistic calculations (``numerical experiment'') of the torsional rigidity bars made of several FCC metals modeled using the embedded atom method. Very good agreement is obtained between theory and simulation. The framework presented here can aid the development of design methodologies for nanoscale structural elements without the need for full scale atomistic simulations.

Evolutionary algorithms - how to cope with plateaus of constant fitness and when to reject strings of the same fitness

Abstract: The most simple evolutionary algorithm (EA), the so-called (1 + 1) EA, accepts an offspring if its fitness is at least as large (in the case of maximization) as the fitness of its parent. The variant (1 + 1)* EA only accepts an offspring if its fitness is strictly larger than the fitness of its parent. Here, two functions related to the class of long-path functions are presented such that the (1 + 1) EA maximizes one in polynomial time and needs exponential time for the other while the (1 + 1)* EA has the opposite behavior. These results demonstrate that small changes of an EA may change its behavior significantly. Since the (1 + 1) EA and the (1 + 1)* EA differ only on plateaus of constant fitness, the results also show how EAs behave on such plateaus. The (1 + 1) EA can pass a path of constant fitness and polynomial length in polynomial time. Finally, for these functions, it is shown that local performance measures like the quality gain and the progress rate do not describe the global behavior of EAs.

A modified constrained constant modulus approach to blind adaptive multiuser detection

Abstract: An alternative blind adaptive multiuser detection is investigated based on modified constrained constant modulus (CM) criterion. It is shown that the performance of a CM-based receiver is limited by the received power of the desired user. In this paper, we show that the limitation can be avoided using the noncanonical constraint CM criterion and that in the presence of channel noise the modified CM criterion function is strictly convex by properly selecting some constant. With analyzing the extrema of the cost function, we point out how to select the constant. Moreover, a simple stochastic gradient algorithm for implementing our scheme is presented, and the convergence properties of the algorithm are analyzed. Simulation examples are given to demonstrate the performance of the proposed scheme.

Distinct Distances in the Plane

Abstract: It is shown that every set of n points in the plane has an element from which there are at least cn 6/7 other elements at distinct distances, where c>0 is a constant. This improves earlier results of Erd?s, Moser, Beck, Chung, Szemeredi, Trotter, and Szekely.

Sequencing JIT Mixed-Model Assembly Lines Under Station-Load and Part-Usage Constraints

Abstract: This paper deals with two most important problems, from both practical and theoretical standpoints, arising in sequencing mixed-model assembly lines. Such lines have become core components of modern repetitive manufacturing, and just-in-time (JIT) manufacturing in particular. One problem is to keep the usage rate of all parts fed into the final assembly as constant as possible (the "level-scheduling problem"), while the other is to keep the line's workstation loads as constant as possible (the "car-sequencing problem"). In this paper the combined problem is formulated as a single-integer programming model. The LP-relaxation of this model is solved by column-generation techniques. The results of an experimental evaluation show that the lower bounds are tight.

Connected sums of constant mean curvature surfaces in Euclidean 3 space

Abstract: We establish a general `gluing theorem', which states roughly that if two nondegenerate constant mean curvature surfaces are juxtaposed, so that their tangent planes are parallel and very close to one another, but oppositely oriented, then there is a new constant mean curvature surface quite near to this configuration (in the Hausdorff topology), but which is a topological connected sum of the two surfaces. Here nondegeneracy refers to the invertibility of the linearized mean curvature operator. This paper treats the simplest context for our result namely when the surfaces are compact with nonempty boundary, however the construction applies in the complete, noncompact setting as well. The surfaces we produce here are nondegenerate for generic choices of the free parameters in the construction.

Transport Properties in Drying of Solids

Abstract: The transport properties in convection drying of industrially prepared roof tile clay slab were investigated on a laboratory scale in a temperature interval from 30°C to 70°C. The velocity and relative humidity of the drying air was kept constant. Obtained drying data were approximated with different mathematical models. Applied models analysis enables evaluation of the main transport properties: effective diffusion coefficient, mass and heat transfer coefficients, thermal conductivity, drying constant, and exponential model parameters. Based on Biot number value, the main transport mechanism was defined. Very small Biot numbers, less than 0.1, for both heat and mass transfer, indicates that the heat and mass transfer are externally controlled. Evaluated parameters were connected with process condition and the drying constant. The air temperature strongly influences the drying kinetics, transport properties and exponential model parameters. Increase of temperature cause exponential increase of effective diffusion coefficient, thermal diffusivity and heat transfer coefficient, while values of parameter k and drying constant increases linearly. Exponential model parameter, n, is independent of temperature. It was found that the drying constant is essentially a combination of transport properties, transfer coefficients, geometry of the sample and experimental conditions.

Constant CFM control algorithm for an air moving system utilizing a centrifugal blower driven by an induction motor

Abstract: A method and apparatus for achieving constant air flow rate economically utilizes an induction blower motor with control settings determining the motor excitation voltage. A memory stores, for a variety of motor speeds, a graph of the speeds plotted against a proportionality constant of flow rate to fan speed for the selected motor system on one axis and motor control settings on the other axis. The only monitoring necessary to achieve the constant flow rate is thus the sensing of fan rotational speed. The measured fan speed is compared against the proportionality constant needed for the selected constant air flow rate and a motor excitation voltage is derived to achieve that proportionality constant. When the system load changes significantly, thereby causing significant fan speed change, a cascaded control loop is used whereby the speed changed induced by each control voltage adjustment is monitored until the desired constant flow rate is again attained at the new load level.

Secure Distributed Linear Algebra in a Constant Number of Rounds

Abstract: Consider a network of processors among which elements in a finite field K can be verifiably shared in a constant number of rounds. Assume furthermore constant-round protocols are available for generating random shared values, for secure multiplication and for addition of shared values. These requirements can be met by known techniques in all standard models of communication. In this model we construct protocols allowing the network to securely solve standard computational problems in linear algebra. In particular, we show how the network can securely, efficiently and in constant-round compute determinant, characteristic polynomial, rank, and the solution space of linear systems of equations. Constant round solutions follow for all problems which can be solved by direct application of such linear algebraic methods, such as deciding whether a graph contains a perfect match. If the basic protocols (for shared random values, addition and multiplication) we start from are unconditionally secure, then so are our protocols. Our results offer solutions that are significantly more efficient than previous techniques for secure linear algebra, they work for arbitrary fields and therefore extend the class of functions previously known to be computable in constant round and with unconditional security. In particular, we obtain an unconditionally secure protocol for computing a function f in constant round, where the protocol has complexity polynomial in the span program size of f over an arbitrary finite field.

Discretized Lyapunov functional for systems with distributed delay and piecewise constant coefficients

Abstract: The stability problem for systems with distributed delay is considered using discretized Lyapunov functional. The coefficients associated with the distributed delay are assumed to be piecewise constant, and the discretization mesh may be non-uniform. The resulting stability criteria are written in the form of linear matrix inequality. Numerical examples are also provided to illustrate the effectiveness of the method. The basic idea can be extended to a more general setting with more involved formulation.

Power injected in dissipative systems and the fluctuation theorem

Abstract: We consider three examples of dissipative dynamical systems involving many degrees of freedom, driven far from equilibrium by a constant or time dependent forcing. We study the statistical properties of the injected and dissipated power as well as the fluctuations of the total energy of these systems. The three systems under consideration are: a shell model of turbulence, a gas of hard spheres colliding inelastically and excited by a vibrating piston, and a Burridge-Knopoff spring-block model. Although they involve different types of forcing and dissipation, we show that the statistics of the injected power obey the “fluctuation theorem" demonstrated in the case of time reversible dissipative systems maintained at constant total energy, or in the case of some stochastic processes. Although this may be only a consequence of the theory of large deviations, this allows a possible definition of “temperature" for a dissipative system out of equilibrium. We consider how this “temperature" scales with the energy and the number of degrees of freedom in the different systems under consideration.

Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces

Abstract: In this paper we study curves with constant geodesic curvature in rotationally symmetric complete surfaces. Under monotonicity conditions on the Gauss curvature we classify the closed embedded ones in planes, cylinders, spheres and projective planes. We also distinguish the stable ones, i.e., the second order minima of perimeter while keeping constant the area enclosed. We prove existence and nonexistence of isoperimetric domains, and we show the isoperimetric domains when they exist.

De)Stabilization of an extra dimension due to a Casimir force

Abstract: We study the stabilization of one spatial dimension in (p+1+1)-dimensional spacetime in the presence of p-dimensional brane(s), a bulk cosmological constant and the Casimir force generated by a conformally coupled scalar field. We find general static solutions to the metric which require the fine-tuning of the interbrane distance and the bulk cosmological constant (leaving the two brane tensions as free parameters) corresponding to a vanishing effective cosmological constant and a constant radion field. Taking these solutions as a background configuration, we perform a dimensional reduction and study the effective theory in the case of one- and two-brane configurations. We show that the radion field can have a positive mass squared, which corresponds to a stabilization of the extra dimension, only for a repulsive nature of the Casimir force. This type of solution requires the presence of a negative tension brane. The solutions with one or two positive tension branes arising in this theory turn out to have negative radion mass squared, and therefore are not stable.